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Message: <blockquote data-quote="orsal" data-source="post: 3644034" data-attributes="member: 16016">The catch is that sometimes, to make a mathematical problem easier, you sometimes need to cleverly restate it in superficially different but logically equivalent terms. The key idea that Nifft was exploiting is that "or" and "and" are duals -- if you replace everything with its complement (i.e. put "not" in front of everything) then they switch places.NOT (X OR Y) is the same as (NOT X) AND (NOT Y)NOT (X AND Y) is the same as (NOT X) OR (NOT Y)Which would you rather compute. "OR" probabilities are only straightforward if the events are mutually exclusive (in which case you can just add probabilities: prob(3 on a d6)=1/6, prob(5 on a d6)=1/6, so prob(3 or 5 on a d6)=2/6. But that's for a single die -- if you're rolling different dice, outcomes won't be mutually exclusive.In contrast, "AND" probabilities are straightforward to calculate if the events are independent, i.e. knowing what happens with one of them won't affect the probability of the other(s). Events associated with different dice are independent -- if you know the first one came up 2, it won't change the probabilities of the next one. So the probabilities involved in this problem are independent.Once you see this, you know you'd rather think about "AND" combinations than "OR" combinations. So, Nifft rephrased the question in terms of the opposite events, and got the answer quickly. It's a trick that comes up in any beginning probability theory course.</blockquote>

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